Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas

Eliezer Hameiri

Research output: Contribution to journalArticle

Abstract

Dedicated to Professor Harold Weitzner on the occasion of his retirement "Say to wisdom 'you are my sister,' and to insight 'you are my relative.'" - Proverbs 7:4 Based on an extension to plasmas of Ertel's classical vorticity theorem in fluid dynamics, it is shown that for each species in a multi-fluid plasma there can be constructed a set of nested surfaces that have this species' fluid particles confined within them. Variational formulations for the plasma evolution and its equilibrium states are developed, based on the new surfaces and all of the dynamical conservation laws associated with them. It is shown that in the general equilibrium case, the energy principle lacks a minimum and cannot be used as a stability criterion. A limit of the variational integral yields the two-fluid Hall-magnetohydrodynamic (MHD) model. A further special limit yields MHD equilibria and can be used to approximate the equilibrium state of a Hall-MHD plasma in a perturbative way.

Original languageEnglish (US)
Article number092503
JournalPhysics of Plasmas
Volume20
Issue number9
DOIs
StatePublished - Sep 2013

Fingerprint

vorticity
theorems
magnetohydrodynamics
fluids
retirement
fluid dynamics
conservation laws
formulations
energy

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas. / Hameiri, Eliezer.

In: Physics of Plasmas, Vol. 20, No. 9, 092503, 09.2013.

Research output: Contribution to journalArticle

@article{d504b654e10d4b99881d9329157538dd,
title = "Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas",
abstract = "Dedicated to Professor Harold Weitzner on the occasion of his retirement {"}Say to wisdom 'you are my sister,' and to insight 'you are my relative.'{"} - Proverbs 7:4 Based on an extension to plasmas of Ertel's classical vorticity theorem in fluid dynamics, it is shown that for each species in a multi-fluid plasma there can be constructed a set of nested surfaces that have this species' fluid particles confined within them. Variational formulations for the plasma evolution and its equilibrium states are developed, based on the new surfaces and all of the dynamical conservation laws associated with them. It is shown that in the general equilibrium case, the energy principle lacks a minimum and cannot be used as a stability criterion. A limit of the variational integral yields the two-fluid Hall-magnetohydrodynamic (MHD) model. A further special limit yields MHD equilibria and can be used to approximate the equilibrium state of a Hall-MHD plasma in a perturbative way.",
author = "Eliezer Hameiri",
year = "2013",
month = "9",
doi = "10.1063/1.4820769",
language = "English (US)",
volume = "20",
journal = "Physics of Plasmas",
issn = "1070-664X",
publisher = "American Institute of Physics Publising LLC",
number = "9",

}

TY - JOUR

T1 - Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas

AU - Hameiri, Eliezer

PY - 2013/9

Y1 - 2013/9

N2 - Dedicated to Professor Harold Weitzner on the occasion of his retirement "Say to wisdom 'you are my sister,' and to insight 'you are my relative.'" - Proverbs 7:4 Based on an extension to plasmas of Ertel's classical vorticity theorem in fluid dynamics, it is shown that for each species in a multi-fluid plasma there can be constructed a set of nested surfaces that have this species' fluid particles confined within them. Variational formulations for the plasma evolution and its equilibrium states are developed, based on the new surfaces and all of the dynamical conservation laws associated with them. It is shown that in the general equilibrium case, the energy principle lacks a minimum and cannot be used as a stability criterion. A limit of the variational integral yields the two-fluid Hall-magnetohydrodynamic (MHD) model. A further special limit yields MHD equilibria and can be used to approximate the equilibrium state of a Hall-MHD plasma in a perturbative way.

AB - Dedicated to Professor Harold Weitzner on the occasion of his retirement "Say to wisdom 'you are my sister,' and to insight 'you are my relative.'" - Proverbs 7:4 Based on an extension to plasmas of Ertel's classical vorticity theorem in fluid dynamics, it is shown that for each species in a multi-fluid plasma there can be constructed a set of nested surfaces that have this species' fluid particles confined within them. Variational formulations for the plasma evolution and its equilibrium states are developed, based on the new surfaces and all of the dynamical conservation laws associated with them. It is shown that in the general equilibrium case, the energy principle lacks a minimum and cannot be used as a stability criterion. A limit of the variational integral yields the two-fluid Hall-magnetohydrodynamic (MHD) model. A further special limit yields MHD equilibria and can be used to approximate the equilibrium state of a Hall-MHD plasma in a perturbative way.

UR - http://www.scopus.com/inward/record.url?scp=84885027332&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885027332&partnerID=8YFLogxK

U2 - 10.1063/1.4820769

DO - 10.1063/1.4820769

M3 - Article

VL - 20

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 9

M1 - 092503

ER -